The seminar is joint for the division of Analysis and Probability and its main themes are Mathematical Physics, Probability Theory and Harmonic and Functional Analysis. The seminar is encouraged to be aimed at a broader audience, but it may be of a more specialised nature when indicated in the last line of the abstract.
The talks in the seminar are usually 60 minutes, including questions.

At the moment, the seminar takes place via Zoom. See schedule below for links to Zoom meetings.

Should you have any questions or suggestions, feel free to email one of the organizers Jakob Björnberg (jakobbj 'at' chalmers.se, Probability Theory), Erik Broman (broman 'at' chalmers.se, Probability Theory) or Genkai Zhang (genkai 'at' chalmers.se, Analysis).

Should you have any questions or suggestions, feel free to email one of the organizers Jakob Björnberg (jakobbj 'at' chalmers.se, Probability Theory), Erik Broman (broman 'at' chalmers.se, Probability Theory) or Genkai Zhang (genkai 'at' chalmers.se, Analysis).

**Coming seminars****2021-03-09 at 13:15**

Irina Pettersson (Chalmers)

Irina Pettersson (Chalmers)

*Multiscale analysis of myelinated axons*

Starting from the late 1990s, peripheral nerve stimulation has been a commonly used method for localizing nerves before the injection of local anesthetic. It has been used both for a single-injection technique, and in a combination with ultrasound guidance during the insertion of continuous nerve block catheters.

A neuron is a basic structural unit of the nervous system, and one needs to know how a signal propagates along neurons to be able to simulate the excitation. We focus on the multiscale modeling of a myelinated axon. Taking into account the microstructure with alternating myelinated parts and nodes Ranvier, we derive an effective nonlinear cable equation describing the potential propagation along a single axon. Cable equations used in electrophysiology are traditionally formulated based on an equivalent circuits consisting of a capacitor in parallel with a conductor. Such models, however, do not take into account the geometry of the myelin sheath. I will also discuss some recent results about the multiscale analysis of a bundle consisting of many myelinated axons.

(Joint work with V. Rybalko and C. Jerez-Hanckes.)

The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organizers (please inform us who you are).

**2021-03-16 at 13:15**

Gabor Pete (Budapest)

Gabor Pete (Budapest)

The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organizers (please inform us who you are).

**2021-03-23 at 13:15**

Nizar Demni (Marseille)

Nizar Demni (Marseille)

The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organizers (please inform us who you are).

**2021-03-30 at 13:15**

Henna Koivusalo (Bristol)

Henna Koivusalo (Bristol)

The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organizers (please inform us who you are).

**2021-04-06 at 13:15**

Eusebio Gardella (Munster)

Eusebio Gardella (Munster)

The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organizers (please inform us who you are).

**2021-04-13 at 13:15**

Isabelle Tristani (ENS, Paris)

Isabelle Tristani (ENS, Paris)

The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organizers (please inform us who you are).

**2021-04-20 at 13:15**

Eviatar Procaccia (Technion, Israel)

Eviatar Procaccia (Technion, Israel)

*Dimension of Stationary Hastings Levitov*

The Hastings-Levitov process is a planar aggregation process defined by a composition of conformal maps, in which at every time a new particle attaches itself to the existing cluster at a point which is determined by the harmonic measure. The main advantage of this model is that its direct connection to complex analysis makes it tractable. The main disadvantage is non-physical behaviour of the particle sizes. In this talk I will present a new half-plane variant of the Hastings-Levitov model, and will demonstrate that our variant, called the Stationary Hastings-Levitov, maintains the tractability of the original model, while avoiding the non-physical behavior of the particle sizes. Thus this model can be seen as a tractable off-lattice Diffusion Limited Aggregation (DLA). Our main result concerns exact growth bounds and fractal dimension.

Based on joint work with Noam Berger and Amanda Turner

The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organizers (please inform us who you are).

**2021-04-27 at 13:15**

Augusto Teixera (IMPA, Brazil)

Augusto Teixera (IMPA, Brazil)

The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organizers (please inform us who you are).

**2021-06-01 at 13:15**

Jacob van den Berg (CWI, Amsterdam)

Jacob van den Berg (CWI, Amsterdam)

The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organizers (please inform us who you are).

**Previous seminars**

**2021-01-19 at 13:15**

Masatoshi Noumi (Kobe/KTH)

Masatoshi Noumi (Kobe/KTH)

*Eigenfunctions for the elliptic Ruijsenaars difference operators*

On the basis of a collaboration with Edwin Langmann (KTH) and Junichi Shiraishi (Tokyo), I report recent progresses in understanding the joint eigenfunctions for the commuting family of elliptic Ruijsenaars difference operators. After reviewing some basic known facts regarding the Macdonald-Ruijsenaars operators in the trigonometric case, I propose two classes of joint eigenfunctions for the elliptic Ruijsenaars operators:

(A) symmetric eigenfunctions around the torus that deform Macdonald polynomials, and

(B) asymptotically free eigenfunctions in a certain asymptotic domain.

**2021-01-26 at 13:15**

Pál Galicza (Budapest)

Pál Galicza (Budapest)

*Sparse reconstruction in spin systems*

We consider a sequence of transitive spin systems on the sequence of finite graphs $G_n(V_n, E_n)$ and we are investigating the following question: Is there a non-degenerate sequence of transitive Boolean functions $f_n: \{-1,1\}^{V_n} \longrightarrow \{-1,1\}$ such that there is some sequence of subset $U_n$ of the vertex set, such that $|U_n|=o(V_n)$ but knowing the spins in $U_n$ give significant information on the value of $f_n$. Our main focus are product and Ising measures. We start by showing that no sparse reconstruction is possible for product measure. As for the Ising model it turns out that for supercritical and critical Ising measures on any graph sequence, magnetisation can be reconstructed from some small subsets of spins. For the subcritical case we present some results suggesting that no such reconstruction is possible. In particular, we show using information theoretical methods that there is no sparse reconstruction for the sequence of subcritical Curie-Weiss models. Reducing no sparse reconstruction to rapid mixing of certain block dynamics we prove the same for the Ising model on the sequence $\mathbb{Z}^2_n$ . Joint work with Gábor Pete.

**2021-02-02 at 16:15**(Note the unusual time)

**Simon Larson (Caltech)**

*Lieb–Thirring inequalities beyond Pauli's exclusion principle*

We propose a general strategy to derive kinetic Lieb–Thirring inequalities for scale-covariant quantum many-body systems under `weak' assumptions. In particular, we do not assume the validity of Pauli's exclusion principle. As an application, we obtain a generalization of the Lieb–Thirring inequality to wave functions vanishing on the diagonal set of the configuration space.

Based on joint work with Douglas Lundholm and Phan Thành Nam.

**2021-02-09 at 13:15**

Diane Holcomb (KTH)

Diane Holcomb (KTH)

*The stochastic Airy operator and an interesting eigenvalue process*

The Gaussian ensembles, originally introduced by Wigner may be generalized to an n-point ensemble called the beta-Hermite ensemble. As with the original ensembles we are interested in studying the local behavior of the eigenvalues. At the edges of the ensemble the rescaled eigenvalues converge to the Airy_beta process which for general beta is characterized as the eigenvalues of a certain random differential operator called the stochastic Airy operator (SAO). In this talk I will give a short introduction to the Stochastic Airy Operator and the proof of convergence of the eigenvalues, before introducing another interesting eigenvalue process. This process can be characterized as a limit of eigenvalues of minors of the tridiagonal matrix model associated to the beta-Hermite ensemble as well as the process formed by the eigenvalues of the SAO under a restriction of the domain. This is joint work with Angelica Gonzalez.

**2021-02-17 at 15:15**

Olof Sisask (Stockholm)(Joint with Number Theory -- hence the unusual time and day)

Olof Sisask (Stockholm)

*Breaking the logarithmic barrier in Roth's theorem*

We present an improvement to Roth's theorem on arithmetic progressions, implying the first non-trivial case of a conjecture of Erdős: if a subset A of {1,2,3,...} is not too sparse, in that the sum of its reciprocals diverges, then A must contain infinitely many three-term arithmetic progressions. Although a problem in number theory and combinatorics on the surface, it turns out to have fascinating links with geometry, harmonic analysis and probability, and we shall aim to give something of a flavour of this.

**2021-02-23 at 13:15**

Noam Berger (Munich)

Noam Berger (Munich)

*Harnack inequalities for difference equations with random balanced coefficients.*

We consider difference equations with balanced i.i.d. coefficients which are not necessarily elliptic, and prove a (large scale) elliptic Harnack inequality with an optimal Harnack constant for non-negative solutions of such equations. We then turn to prove a parabolic Harnack inequality in the same setting, and prove it under the additional condition of a (relatively mild) growth condition. We show by example that the growth condition is necessary. I will start the talk with a general background on Harnack inequalities and their significance in (analysis and) probability theory, then I will sketch the main ingredients of the proofs and then I will show a few applications.

The talk is based on joint works with Moran Cohen, David Criens, Jean-Dominique Deuschel and Xiaoqin Guo.

**2021-03-02 at 13:15**

Jan Felipe van Diejen (Universidad de Talca, Chile)

Jan Felipe van Diejen (Universidad de Talca, Chile)

*Quantum eigenfunctions and bispectral duality for Inozemtsev's Toda chain with boundary interactions*

In the late nineteen eighties, Inozemtsev observed by means of an explicit Lax-pair representation that the Toda chain remains integrable when coupled to a Pöschl-Teller potential. Previous boundary potentials of Morse type that were known to preserve the integrability of the Toda chain arise in his picture as limiting cases. In this talk we report on some recent results in collaboration with Erdal Emsiz concerning the eigenfunctions of the quantum version of Inozemtsev's Toda chain, with an emphasis on bispectrality.